Understanding ratios between exponents, me understand.

[christian0710]

1. I need some help understanding ratios between 2 numbers/quantities og exponents:

2.Here is the problem, When you take the ratio between 100grams and 1000grams it is 100g/1000g = 0,10 and you can convert this to kilos 0,1kg/1kg = 0,10 and the ratio stays intact, that makes sense. But let's say the relationship between the mass of the egg a bird lays and the mass of the bird is given by M_egg = c*M_bird^(0.77). Then the constant c is a ratio between M_egg/M_bird^0,77. If the bird weighs 1.5kg and the egg weighs 0,070kg, then I get two completely different results if I first calculate the ratio in grams and efter that in kg. Why is that? And how do you work around it?

In grams M_egg/M_bird^077 = 0,070kg/1.5^(0,77)kg = 0.051
in kg M_egg/M_bird^077 = 70g/1500^(0,77)5 = 0.025

Is there some fundamental theory i need to understand about exponents that i missed out on?

 

[SteamKing]

1. I need some help understanding ratios between 2 numbers/quantities og exponents:

2.Here is the problem, When you take the ratio between 100grams and 1000grams it is 100g/1000g = 0,10 and you can convert this to kilos 0,1kg/1kg = 0,10 and the ratio stays intact, that makes sense. But let's say the relationship between the mass of the egg a bird lays and the mass of the bird is given by M_egg = c*M_bird^(0.77). Then the constant c is a ratio between M_egg/M_bird^0,77. If the bird weighs 1.5kg and the egg weighs 0,070kg, then I get two completely different results if I first calculate the ratio in grams and efter that in kg. Why is that? And how do you work around it?

In grams M_egg/M_bird^077 = 0,070kg/1.5^(0,77)kg = 0.051
in kg M_egg/M_bird^077 = 70g/1500^(0,77)5 = 0.025

Is there some fundamental theory i need to understand about exponents that i missed out on?

Not really. But since the masses of the egg and the bird can be expressed in different units, this implies that the constant 'c' also has some units, which may not be stated. As long as you use the proper units for the masses of the egg and bird with a particular value of 'c', the formula will work. Otherwise, ...

 

[haruspex]

As long as you use the proper units for the masses of the egg and bird with a particular value of 'c', the formula will work. Otherwise, ...

... it will also work if you include the units for the given value of c. In the present case, the units would be something like kg^0.23 or gm^0.23, etc. E.g. 0.22 gm^0.23 = 0.045 kg^0.23.